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Properties

Label 3040.2.f
Level $3040$
Weight $2$
Character orbit 3040.f
Rep. character $\chi_{3040}(1521,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $2$
Sturm bound $960$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 3040 = 2^{5} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3040.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(960\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3040, [\chi])\).

Total New Old
Modular forms 496 72 424
Cusp forms 464 72 392
Eisenstein series 32 0 32

Trace form

\( 72 q - 8 q^{7} - 72 q^{9} - 8 q^{23} - 72 q^{25} + 48 q^{39} + 40 q^{47} + 72 q^{49} - 16 q^{55} - 40 q^{63} + 16 q^{71} - 80 q^{79} + 88 q^{81} - 96 q^{87} - 16 q^{89} + 16 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(3040, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3040.2.f.a 3040.f 8.b $28$ $24.275$ None 760.2.f.a \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$
3040.2.f.b 3040.f 8.b $44$ $24.275$ None 760.2.f.b \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(3040, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3040, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(608, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(760, [\chi])\)\(^{\oplus 3}\)